Abstract

We put forward a method to easily generate a single or a sequence of fully developed speckle patterns with pre-defined correlation distribution by utilizing the principle of coherent imaging. The few-to-one mapping between the input correlation matrix and the correlation distribution between simulated speckle patterns is realized and there is a simple square relationship between the values of these two correlation coefficient sets. This method is demonstrated both theoretically and experimentally. The square relationship enables easy conversion from any desired correlation distribution. Since the input correlation distribution can be defined by a digital matrix or a gray-scale image acquired experimentally, this method provides a convenient way to simulate real speckle-related experiments and to evaluate data processing techniques.

© 2016 Optical Society of America

Full Article  |  PDF Article
OSA Recommended Articles
Optimization of fringe pattern calculation with direct correlations in speckle interferometry

Douglas R. Schmitt and R. W. Hunt
Appl. Opt. 36(34) 8848-8857 (1997)

The copula: a tool for simulating speckle dynamics

Donald D. Duncan and Sean J. Kirkpatrick
J. Opt. Soc. Am. A 25(1) 231-237 (2008)

Retrieving controlled motion parameters using two speckle pattern analysis techniques: spatiotemporal correlation and the temporal history speckle pattern

Rana Nassif, Christelle Abou Nader, Fabrice Pellen, Guy Le Brun, Marie Abboud, and Bernard Le Jeune
Appl. Opt. 52(31) 7564-7569 (2013)

References

  • View by:
  • |
  • |
  • |

  1. D. D. Duncan and S. J. Kirkpatrick, “The copula: a tool for simulating speckle dynamics,” J. Opt. Soc. Am. A 25(1), 231–237 (2008).
    [Crossref] [PubMed]
  2. S. J. Kirkpatrick, D. D. Duncan, and E. M. Wells-Gray, “Detrimental effects of speckle-pixel size matching in laser speckle contrast imaging,” Opt. Lett. 33(24), 2886–2888 (2008).
    [Crossref] [PubMed]
  3. D. D. Duncan and S. J. Kirkpatrick, “Algorithms for simulation of speckle (laser and otherwise),” Biomedical Optics (BiOS) (Optical Society of America, 2008), pp 685505.
  4. O. B. Thompson and M. K. Andrews, “Tissue perfusion measurements: multiple-exposure laser speckle analysis generates laser Doppler-like spectra,” J. Biomed. Opt. 15(2), 027015 (2010).
    [Crossref] [PubMed]
  5. H. Zhang, P. Li, N. Feng, J. Qiu, B. Li, W. Luo, and Q. Luo, “Correcting the detrimental effects of nonuniform intensity distribution on fiber-transmitting laser speckle imaging of blood flow,” Opt. Express 20(1), 508–517 (2012).
    [Crossref] [PubMed]
  6. V. Nascov, C. Samoilă, and D. Ursuţiu, “Fast computation algorithms for speckle pattern simulation,” AIP Conf. Proc. 1564, 217–222 (2013).
    [Crossref]
  7. H. Fujii, J. Uozumi, and T. Asakura, “Computer simulation study of image speckle patterns with relation to object surface profile,” J. Opt. Soc. Am. 66(11), 1222–1236 (1976).
    [Crossref]
  8. D. M. Manfred Gilli and E. Schumann, Numerical Methods and Optimization in Finance (Academic Press, 2011).
  9. J. Goodman, Introduction to Fourier Optics (Roberts and Company Publishers, 2004).
  10. J. W. Goodman, Speckle Phenomena in Optics: Theory and Applications (Roberts & Co, 2007).
  11. J. W. Goodman, Statistical Optics, 2nd ed. (Wiley, 2015).
  12. 'Normal Product Distribution', Mathworld.
  13. D. D. Duncan and S. J. Kirkpatrick, “Can laser speckle flowmetry be made a quantitative tool?” J. Opt. Soc. Am. A 25(8), 2088–2094 (2008).
    [Crossref] [PubMed]
  14. V. Rajan, B. Varghese, T. G. van Leeuwen, and W. Steenbergen, “Speckle size and decorrelation time; space–time correlation analysis of coherent light dynamically scattered from turbid media,” Opt. Commun. 281(6), 1755–1760 (2008).
    [Crossref]
  15. P. Zakharov, A. Völker, A. Buck, B. Weber, and F. Scheffold, “Quantitative modeling of laser speckle imaging,” Opt. Lett. 31(23), 3465–3467 (2006).
    [Crossref] [PubMed]

2013 (1)

V. Nascov, C. Samoilă, and D. Ursuţiu, “Fast computation algorithms for speckle pattern simulation,” AIP Conf. Proc. 1564, 217–222 (2013).
[Crossref]

2012 (1)

2010 (1)

O. B. Thompson and M. K. Andrews, “Tissue perfusion measurements: multiple-exposure laser speckle analysis generates laser Doppler-like spectra,” J. Biomed. Opt. 15(2), 027015 (2010).
[Crossref] [PubMed]

2008 (4)

2006 (1)

1976 (1)

Andrews, M. K.

O. B. Thompson and M. K. Andrews, “Tissue perfusion measurements: multiple-exposure laser speckle analysis generates laser Doppler-like spectra,” J. Biomed. Opt. 15(2), 027015 (2010).
[Crossref] [PubMed]

Asakura, T.

Buck, A.

Duncan, D. D.

Feng, N.

Fujii, H.

Kirkpatrick, S. J.

Li, B.

Li, P.

Luo, Q.

Luo, W.

Nascov, V.

V. Nascov, C. Samoilă, and D. Ursuţiu, “Fast computation algorithms for speckle pattern simulation,” AIP Conf. Proc. 1564, 217–222 (2013).
[Crossref]

Qiu, J.

Rajan, V.

V. Rajan, B. Varghese, T. G. van Leeuwen, and W. Steenbergen, “Speckle size and decorrelation time; space–time correlation analysis of coherent light dynamically scattered from turbid media,” Opt. Commun. 281(6), 1755–1760 (2008).
[Crossref]

Samoila, C.

V. Nascov, C. Samoilă, and D. Ursuţiu, “Fast computation algorithms for speckle pattern simulation,” AIP Conf. Proc. 1564, 217–222 (2013).
[Crossref]

Scheffold, F.

Steenbergen, W.

V. Rajan, B. Varghese, T. G. van Leeuwen, and W. Steenbergen, “Speckle size and decorrelation time; space–time correlation analysis of coherent light dynamically scattered from turbid media,” Opt. Commun. 281(6), 1755–1760 (2008).
[Crossref]

Thompson, O. B.

O. B. Thompson and M. K. Andrews, “Tissue perfusion measurements: multiple-exposure laser speckle analysis generates laser Doppler-like spectra,” J. Biomed. Opt. 15(2), 027015 (2010).
[Crossref] [PubMed]

Uozumi, J.

Ursutiu, D.

V. Nascov, C. Samoilă, and D. Ursuţiu, “Fast computation algorithms for speckle pattern simulation,” AIP Conf. Proc. 1564, 217–222 (2013).
[Crossref]

van Leeuwen, T. G.

V. Rajan, B. Varghese, T. G. van Leeuwen, and W. Steenbergen, “Speckle size and decorrelation time; space–time correlation analysis of coherent light dynamically scattered from turbid media,” Opt. Commun. 281(6), 1755–1760 (2008).
[Crossref]

Varghese, B.

V. Rajan, B. Varghese, T. G. van Leeuwen, and W. Steenbergen, “Speckle size and decorrelation time; space–time correlation analysis of coherent light dynamically scattered from turbid media,” Opt. Commun. 281(6), 1755–1760 (2008).
[Crossref]

Völker, A.

Weber, B.

Wells-Gray, E. M.

Zakharov, P.

Zhang, H.

AIP Conf. Proc. (1)

V. Nascov, C. Samoilă, and D. Ursuţiu, “Fast computation algorithms for speckle pattern simulation,” AIP Conf. Proc. 1564, 217–222 (2013).
[Crossref]

J. Biomed. Opt. (1)

O. B. Thompson and M. K. Andrews, “Tissue perfusion measurements: multiple-exposure laser speckle analysis generates laser Doppler-like spectra,” J. Biomed. Opt. 15(2), 027015 (2010).
[Crossref] [PubMed]

J. Opt. Soc. Am. (1)

J. Opt. Soc. Am. A (2)

Opt. Commun. (1)

V. Rajan, B. Varghese, T. G. van Leeuwen, and W. Steenbergen, “Speckle size and decorrelation time; space–time correlation analysis of coherent light dynamically scattered from turbid media,” Opt. Commun. 281(6), 1755–1760 (2008).
[Crossref]

Opt. Express (1)

Opt. Lett. (2)

Other (6)

D. D. Duncan and S. J. Kirkpatrick, “Algorithms for simulation of speckle (laser and otherwise),” Biomedical Optics (BiOS) (Optical Society of America, 2008), pp 685505.

D. M. Manfred Gilli and E. Schumann, Numerical Methods and Optimization in Finance (Academic Press, 2011).

J. Goodman, Introduction to Fourier Optics (Roberts and Company Publishers, 2004).

J. W. Goodman, Speckle Phenomena in Optics: Theory and Applications (Roberts & Co, 2007).

J. W. Goodman, Statistical Optics, 2nd ed. (Wiley, 2015).

'Normal Product Distribution', Mathworld.

Cited By

OSA participates in Crossref's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (9)

Fig. 1
Fig. 1 The relationship between correlation coefficient of speckle patterns and that of the phase matrices.
Fig. 2
Fig. 2 (a) The correlation coefficient of the speckle patterns as a function of r; (b) the probability density function of the speckle pattern.
Fig. 3
Fig. 3 (a) The phase matrix r used in the simulation, (b) the correlation coefficients of the rows between the speckle images generated from W and M1 (c) the correlation distribution of the two simulated speckle images.
Fig. 4
Fig. 4 (a) The flow model. (b) The simulated correlation for the two regions as a function of the frame index. The asterisks mark the correlation coefficients of the stationary area with input values equal to 1; the diamonds represent the correlation coefficients in the Brownian motion region, and the line is a negative exponential function.
Fig. 5
Fig. 5 (a) The correlation coefficients of different segments and different frame indices; (b) the correlation distribution defined by five gray levels. This correlation image and the correlation curves were used to synthesize the 20 speckle patterns; (c) the correlation image calculated from the 1st and the 20th simulated speckle patterns; (d) temporal contrast calculated from the 20 simulated speckle patterns.
Fig. 6
Fig. 6 (a) Denoised temporal contrast from the experiment; (b) four labelled regions based on the temporal contrast image shown in (a); (c) the temporal contrast image calculated from the simulation; (d) correlation coefficients used in the simulation; (e) comparison of the contrast profile along the pixels marked by the dashed line in (c) from the experiment and the simulation after smoothing.
Fig. 7
Fig. 7 Investigation of noise level of the correlation calculated with a kernel size equal to 11 × 11. (a) The subtraction of Fig. 3(a) and the square root of Fig. 3(c); (b) the standard deviation of the simulated correlation coefficients as a function of r; (c) the standard deviation of the simulated correlation as a function of the number of correlation images that are averaged.
Fig. 8
Fig. 8 Single-pixel based correlation coefficient calculated from simulated speckle images. (a) the correlation map when using the matrix shown in Fig. 3(a); (b) the subtraction of the square of Fig. 3(a) and Fig. 8(a); (c) the line profile of the correlation coefficients along the 300th column with different input value of correlation coefficients; (d) the smallest correlation coefficient difference that can be shown in the image domain. In this case the input values of r are equal to 0.01 and 0.03 respectively for the two areas.
Fig. 9
Fig. 9 Demonstration of a simulation using noisy images as the input correlation matrix. (a) the input correlation matrix; (b) the correlation map calculated from synthesized speckle images; (c) the temporal contrast image calculated from the synthesized speckle images.

Equations (16)

Equations on this page are rendered with MathJax. Learn more.

W = r e i Ω 1 + 1 r 2 e i Ω 2
Img ( x , y ) = O b j ( x , y ) H ( x , y )
I = | F 1 ( Img ( x , y ) ) | 2 = | F 1 [ O b j ( x , y ) H ( x , y ) ] | 2
I = | F 1 [ F ( W ) H ( x , y ) ] | 2
I = | F ( W ) | 2
W = r M 1 + 1 r 2 M 2
ρ = ( I W I W ) ( I M 1 I M 1 ) σ ( I W ) σ ( I M 1 )
ρ = I W I M 1 I 2 I 2
I M 1 ( A M 1 A M 2 * + A M 2 A M 1 * ) = 0
ρ = [ r 2 I M 1 + ( 1 r 2 ) I M 2 + r 1 r 2 ( A M 1 A M 2 * + A M 1 * A M 2 ) ] I M 1 I 2 I 2 = r 2 I M 1 2 + ( 1 r 2 ) I M 1 I M 2 + r 1 r 2 I M 1 ( A M 1 A M 2 * + A M 1 * A M 2 ) I 2 I 2
ρ = r 2
ρ = r 2 I M 1 2 + r 1 r 2 I M 1 ( F ( M 1 ) F * ( M 2 ) + F * ( M 1 ) F ( M 2 ) ) I 2 + ( 1 r 2 ) I M 1 I M 2 I 2 1
ρ = r 2
ρ ( 0 , j ) = C o v ( I 0 , I j ) σ ( I 0 ) σ ( I j )
ρ = exp ( τ / τ c )
r = exp ( τ / τ c )

Metrics